Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 9x - 5$ and $ KL = 8x + 3$ Find $JL$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {9x - 5} = {8x + 3}$ Solve for $x$ $ x = 8$ Substitute $8$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 9({8}) - 5$ $ KL = 8({8}) + 3$ $ JK = 72 - 5$ $ KL = 64 + 3$ $ JK = 67$ $ KL = 67$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {67} + {67}$ $ JL = 134$